Real-space Recursion Method Research Articles

Possible magnetic ground state of the half doped perovskite compound R 0.5Ce 0.5CoO 3 (R=Ca, Sr)

By using the unrestricted Hartree–Fock approximation and the real-space recursion method, we have investigated various magnetic structures in an enlarged double cell of the half doped compound R 0.5Ce 0.5CoO 3 (R=Ca, Sr). These include the low-spin state ( LS : t 2 g 5 e g 1 ) , the intermediate-spin state ( IS : t 2 g 4.5 e g 1.5 ) , and the high-spin state ( HS : t 2 g 4 e g 2 ) as well as all possible combinations among these three states. The densities of states are computed and stabilities of various states are analyzed as functions of the model parameters. For a fixed Hund's coupling j, it is shown that the ground state of R 0.5Ce 0.5CoO 3 (R=Ca, Sr) transforms from the antiferromagnetic high-spin state to the ferromagnetically ordered high-spin low-spin state as the crystal-field splitting Dq increases.

Theoretical study of p–d hybridization in Co perovskite

Abstract The real-space recursion method and unrestricted Hartree–Fock approximation have been applied to calculate the density of states of various Co perovskite, CeCoO 3 , SrCoO 3 and Sr 1− x Ce x CoO 3 . We have studied the magnetically ordered states of these Co perovskites in an enlarged double cell, and find its various magnetic structures due to the occupancy of 3d band and its interaction with neighboring Co ions. In this study, we have studied the p–d hybridization of the three Co perovskites, we find t 2g electrons are localized and the flat e g band is responsible for the itinerant behavior, and although the rare earth elements itself contribute little to the DOS at the Fermi energy, the DOS at Fermi energy and the magnetic moment changed consequently because of different valence of Co ions in these compounds and p–d hybridization effect is very important.

Theoretical study on the spin and orbital orderings in Ruddlesden-Popper compound La3-3xCa1+3xMn3O10(0 ≤ x ≤ 1)

In this paper, the spin and orbital orderings of the n = 3 Ruddlesden-Popper (RP) series of compounds La3-3xCa1+3xMn3O10 have been analyzed theoretically for the whole doping range 0 ≤ x ≤ 1, the calculation is based on the unrestricted Hartree-Fock approximation and the real-space recursion method. In agreement with experimental observations, we find that the ground state of La3-3xCa1+3xMn3O10 is ferromagnetic metal at x=0.3 and is G-type antiferromagnetic insulator at x = 1. The ferromagnetic metallic state is sustained for lower doping range 0 ≤ x 0.96. Our study unveils a strong spin-orbital correlation in the ferromagnetic metallic state for doping range 0 ≤ x < 0.39, an orbital ordering transition takes place at x = 0.06 which changes from the nearest-neighbor antiferro-orbital ordering (0 ≤ x < 0.06) to the layer-type antiferro-orbital ordering (0.06 < x < 0.39).

Study on the spin-states of cobalt-based double-layer perovskite Sr2Y0.5Ca0.5Co2O7

The spin-states of cobalt based perovskite compounds depend sensitively on the valence state and local crystal environment of Co ions and the rich physical properties arise from strong coupling among charge, spin, and orbital degrees of freedom. While extensive studies have been carried out in the past, most of them concentrated on the isotropic compound LaCoO3. In this paper, using the unrestricted Hartree-Fock approximation and the real-space recursion method, we have investigated the competition of various magnetically ordered spin-states of anisotropic double-layered perovskite Sr2Y0.5Ca0.5Co2O7. The energy comparison among these states shows that the nearest-neighbor high-spin-intermediate-spin ferromagnetically ordered state is the relevant magnetic ground state of the compound. The magnetic structure and sizes of magnetic moments are consistent with the recent experimental observation.

Theoretical study of the density of states and magnetic properties of electron-doped Sr 1−xCe xCoO 3 compounds

Within the unrestricted Hartree–Fock approximation and the real space recursion method, we calculated the electronic structure of the Sr 1− x Ce x CoO 3 in the whole doping range 0.0⩽ x⩽1.0. Various spin states in an enlarged double cell are investigated and five of them are the ground states at different doping concentration. The magnetic ground state of the doped system takes an intermediate-spin state for x<0.02, a low-spin–intermediate-spin ferromagnetically ordered state for 0.02⩽ x<0.38, and a low-spin–high-spin ferromagnetically ordered state for 0.38⩽ x<0.79. For 0.79⩽ x<0.9, the ground state of the system is the intermediate-spin chain-type antiferromagnetically ordered state, which is followed by the intermediate-spin nearest neighbor antiferromagnetically ordered state up to x=1.0. The densities of states of all magnetic ground states are computed and their electronic and magnetic properties are discussed.

Mechanism of Effects of Rare Earths on Microstructure and Properties at Elevated Temperatures of AZ91 Magnesium Alloy

By using real-space recursion method, the energetics of the undoped and A1 and/or RE atoms doped Σ(1450) <0001> symmetric tilt grain boundaries (GBs) in AZ91 alloys were investigated. Similar calculations were performed on undoped and doped bulk α Mg for comparison. The results showed that A1 atoms segregated at GBs in AZ91 alloys. When RE atoms were added, they also segregated at GBs, and their segregation is stronger than A1 atoms'. Therefore, RE atoms retard the segregation of A1 atoms. Calculations of interaction energy indicated that A1 atoms repelled each other, and could form ordered phase with host Mg atoms. On the contrary to the case of A1, RE atoms attracted each other, they could not form ordered phase with Mg, but could form clusters. Between RE and A1, there existed attractive interaction, and this attractive interaction was the origin of Al 11 RE 3 precipitation. Precipitation of A1 11 RE 3 particles with high melting point and high thermal stability along GB improves high temperature properties of AZ91 alloys.

Effect of electron doping on the magnetic structure of then=3Ruddlesden-Popper compoundCa4−xLaxMn3O10(0⩽x⩽0.2)

The Ruddlesden-Popper series of compounds has fascinating electronic and magnetic properties; the rich phase diagram depends not only on the valence of transition-metal elements but also on their complex crystal structures which cover from two-dimensional anisotropic structures to three-dimensional isotropic structures. In this paper, we concentrate on the intermediate case of $n=3$; the electronic and magnetic structures of ${\mathrm{Ca}}_{4\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{Mn}}_{3}{\mathrm{O}}_{10}$ at small doping $(0\ensuremath{\leqslant}x\ensuremath{\leqslant}0.2)$ have been studied theoretically using the unrestricted Hartree-Fock approximation and the real-space recursion method. In agreement with experiments, we find that the ground state of undoped ${\mathrm{Ca}}_{4}{\mathrm{Mn}}_{3}{\mathrm{O}}_{10}$ is a $G$-type antiferromagnetic state. As doping increases, the ground state changes to the almost degenerate $A1$-type antiferromagnetic state or $A2$-type ferrimagnetic state at $x\ensuremath{\geqslant}0.062$. The weak ferromagnetism is probably associated with the ferrimagnetic property of $A2$-type magnetic ordering.

Recursion method for the quasiparticle structure of a single vortex with induced magnetic order

We use a real-space recursion method to calculate the local density of states (LDOS) within a model that contains both d-wave superconducting and antiferromagnetic order. We focus on the LDOS in the superconducting phase near single vortices with either normal or antiferromagnetic cores. Furthermore, we study the low-energy quasiparticle structure when magnetic vortices operate as pinning centers for surrounding unidirectional spin density waves (stripes). We calculate the Fourier transformed LDOS and show how the energy dependence of relevant Fourier components can be used to determine the nature of the magnetic field-induced order, and predict field-induced LDOS features that can be tested by future scanning tunneling microscopy (STM) experiments.

Effect of Mn+ ion implantation on the Raman spectra of ZnO

Raman measurements have been performed on ZnO bulk materials implanted with 220keV Mn+ ions with various doses from 1015to1017cm2. The results reveal two modes at about 230 and 523cm−1, respectively, which are not observed in unimplanted ZnO. One mode at 230cm−1 is assigned to the acoustic-phonon branch at the zone boundary. Another mode at 523cm−1 is attributed to Zn-related vibration due to Mn incorporation. By using a real-space recursion method, the theoretical calculation indicates that the Zn-related mode originates from the vibration of the Zn atom surrounded with the first nearest neighbor of Mn atoms, where the local Zn-related structures are formed by Mn atoms replacing partially the O atoms in the ZnO crystal lattice.

Theoretical study of the spin and orbital ordered states ofLaBaMn2O5.5

The electronic and magnetic structures of an ordered oxygen-deficient perovskite, ${\mathrm{LaBaMn}}_{2}{\mathrm{O}}_{5.5}$, have been investigated using the unrestricted Hartree-Fock approximation and the real-space recursion method. Among the four metastable spin states found in this paper, the ferromagnetic spin state and the spin-ladder antiferromagnetic state with ferromagnetic coupling along the ladder ($b$ and $c$ axes) and antiferromagnetic coupling perpendicular to the ladder ($a$ axis) are found to have almost the same lowest energies. However, the spin-ladder antiferromagnetic state is further stabilized by the Jahn-Teller distortion of octahedra along the $b$ axis, and the resulting orbital ordering of Mn(1) pyramid/Mn(2) octahedra takes the form of the ${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}∕{d}_{3{y}^{2}\ensuremath{-}{r}^{2}}$ pattern. Our results are consistent with the experimental findings.

Magnetic ground state ofRBaCo2O5.5(R=Tb,Gd)compounds

The oxygen-deficient perovskites $R{\mathrm{BaCo}}_{2}{\mathrm{O}}_{5.5}$ $(R=\mathrm{T}\mathrm{b},\mathrm{}\mathrm{Gd})$ unveil similar magnetic properties; the magnetization $[M(T)]$ demonstrates a sharp cusp near the magnetic transition temperature ${T}_{C}$ and a $1/T$ dependence at low temperature, while the remnant magnetic moments at zero temperature are small $[\ensuremath{\mu}\ensuremath{\approx}(0.05--0.1){\ensuremath{\mu}}_{B}]$ the high temperature effective magnetic moments are rather large $[{\ensuremath{\mu}}_{\mathrm{eff}}\ensuremath{\approx}(4.7--4.9){\ensuremath{\mu}}_{B}].$ We show in this paper that the paramagnetic behavior of R ions and ferrimagnetic ordering of high-spin ${\mathrm{Co}}^{+3}$ ions on both octahedron and pyramid sites can account for all above experimental observations. Our conclusion is based on the calculation within the unrestricted Hartree-Fock approximation and the real-space recursion method. Among the large number of spin and charge ordered states we considered, only the high-spin high-spin antiferromagnetically ordered state, the high-spin intermediate-spin antiferromagnetically ordered state, and the low-spin intermediate-spin ferromagnetically ordered state may become the ground state of the system as $\mathrm{Dq}$ increases. However, only the high-spin high-spin antiferromagnetically ordered state is consistent with the experimental findings.

No evident charge ordering inLa1/2Sr3/2MnO4

Using the unrestricted Hartree-Fock approximation to dealwith the correlation effect of the multiband Hubbard model andthe real-space recursion method to calculate the density of states,we have investigated several assumed spin- and orbital-orderedstates in the layered perovskite La1/2Sr3/2MnO4 in addition to the so-called charge-exchange-type antiferromagnetic (CE-AFM) state observed experimentally. It is found that the Jahn-Teller latticedistortion and anisotropic double-exchange interaction ofeg electrons are responsible for the CE-AFM state withd3x2-r2/d3y2-r2 orbital ordering. Ourstudy shows that there is no evidentcharge modulation inreal space, which is consistent with recent band-structurecalculation (Mahadevan P, Terakura K and Sarma D D2001 Phys. Rev. Lett. 87 066404).We attribute this to the strong double-exchange interaction insidethe quasi-one-dimensional ferromagnetic zigzag chain that is thebasic building block of the CE-AFM state.

Theoretical study of the paramagnetic density of states ofYBaCo2O5

By using the unrestricted Hartree-Fock approximation and the real space recursion method, we have investigated the electronic structures of the antiferromagnetic and paramagnetic states of ${\mathrm{YBaCo}}_{2}{\mathrm{O}}_{5}.$ The random spin is dealt with by the usual binary alloy coherent potential approximation when temperature is above ${T}_{N}$ (N\'eel temperature). It is found that the paramagnetic spectrum width does get broadened in comparison with that of antiferromagnetic state at low temperature due to the delocalization of $\mathrm{Co}\ensuremath{-}d$ electrons resulted from the spin scattering. This also causes a pileup of density of states at Fermi energy. Our results offer a direct connection between the calculated electronic structure and the experimentally observed resistance decrease near ${T}_{N}.$

Spin states of the Co ion in charge-orderedYBaCo2O5

To resolve the spin state in the oxygen-deficient double perovskite ${\mathrm{YBaCo}}_{2}{\mathrm{O}}_{5},$ various spin states in an enlarged supercell (four primitive cells) with ${\mathrm{Co}}^{2+}/{\mathrm{Co}}^{3+}$ charge ordering are investigated within the framework of unrestricted Hartree-Fock approximation. The densities of states are computed using the real-space recursion method and stabilities of various states are analyzed as functions of the model parameters. For a fixed Hund's coupling j, the ground state of ${\mathrm{YBaCo}}_{2}{\mathrm{O}}_{5}$ takes consecutively the antiferromagnetic high-spin state $({\mathrm{Co}}^{2+}\ensuremath{-}{t}_{2g}^{5}{e}_{g}^{2};{\mathrm{Co}}^{3+}\ensuremath{-}{t}_{2g}^{4}{e}_{g}^{2}),$ the charge-uniform ferromagnetic high-spin state, and the charge-uniform ferromagnetic low-spin state as crystal-field splitting $\mathrm{Dq}$ increases. The antiferromagnetic high-spin intermediate-spin ordered state $({\mathrm{Co}}^{2+}\ensuremath{-}{t}_{2g}^{5}{e}_{g}^{2};{\mathrm{Co}}^{3+}\ensuremath{-}{t}_{2g}^{5}{e}_{g}^{1})$ never becomes a ground state within the unrestricted Hartree-Fock approximation. Since the antiferromagnetic high-spin state is the only antiferromagnetic state that is stable in the $(Dq,j)$ space, we conclude that it is the most probable candidate for the ground state, which agrees with experiments.

Magnetic structure of the layered perovskiteLaSrCoO4

By using the unrestricted Hartree-Fock approximation and the real-space recursion method, we have investigated various magnetic structures in an enlarged double cell of layered perovskite ${\mathrm{LaSrCoO}}_{4}.$ These include the low-spin state ${(t}_{2g}^{6}{e}_{g}^{0}),$ the intermediate-spin state ${(t}_{2g}^{5}{e}_{g}^{1}),$ and the high-spin state ${(t}_{2g}^{4}{e}_{g}^{2})$ as well as all possible combinations among these three states. The densities of states are computed and stabilities of various states are analyzed as functions of the model parameters. For a fixed Hund's coupling $j,$ it is shown that the ground state of ${\mathrm{LaSrCoO}}_{4}$ transforms first from the antiferromagnetic high-spin state to the ferromagnetically ordered high-spin low-spin state, and then to the nonmagnetic low-spin state as the crystal-field splitting $\mathrm{Dq}$ increases. The intermediate-spin state never becomes the ground state of ${\mathrm{LaSrCoO}}_{4}.$ In view of the measured effective magnetic moment of ${\ensuremath{\mu}}_{\mathrm{eff}}\ensuremath{\sim}2.6{\ensuremath{\mu}}_{B},$ we conclude that the most probable ground state of ${\mathrm{LaSrCoO}}_{4}$ lies in the regime of ferromagnetically ordered high-spin low-spin state, this state is also consistent with the optical conductivity spectra and neutron-diffraction experiment.

Structural stripe phase effect on band structure in underdoped YBa 2Cu 3O 7−δ

Based on a simple model of structural phase model and tight-binding approximation, we calculated the density of states (DOS) of underdoped YBa 2Cu 3O 7−δ by real-space recursion method. It is found that the partial DOS for Cu and O sites increases obviously due to the occurrence of structural stripe phase separation in underdoped YBCO. This suggests that the structural stripe is unstable in energy. This conclusion is in agreement with the fact that no obvious structural stripe phase separation is observed in underdoped YBCO.

Interplay among charge, spin, and orbital ordering in dopedLaMnO3

The electronic structures of various charge- and orbital-ordered ferromagnetic and antiferromagnetic states have been studied for doped ${\mathrm{La}}_{1\ensuremath{-}x}{A}_{x}{\mathrm{MnO}}_{3} (A=\mathrm{C}\mathrm{a},\mathrm{}\mathrm{Sr}).$ We use the unrestricted Hartree-Fock approximation to treat the correlation effect of the multiband Hubbard model and the real-space recursion method to calculate the density of states. Our study shows that energy scales associated with different types of ordering are very different and the orbital ordering involves the smallest energy scale. This suggests that orbital fluctuation plays a very important role in the low-temperature properties of the doped ferromagnetic state. We also find that all antiferromagnetic states are accompanied by a certain amount of charge ordering, but the strength is much weaker than that predicted by the ionic model because of the strong covalency between the $\mathrm{Mn}\ensuremath{-}d$ and $\mathrm{O}\ensuremath{-}p$ orbitals. From an energy comparison of these states, the obtained magnetic phase diagram is in general agreement with experiments.

Theoretical study on the spin-state transition in dopedLa2-xSrxCoO4

The spin-state transition is an interesting and unresolved problem in layered perovskite La2-xSrxCoO4 under doping, asit involves competition among different magnetic structures. Within the unrestricted Hartree-Fock approximation and using the real space recursion method we have studied the effect of Sr doping on the magnetic and electronic properties of layered perovskite La2CoO4. All configurations in an enlarged double cell among the low-spin (t2g6eg1) and the high-spin (t2g5eg2) states are considered. It is found that the ground state of a doped system takes the antiferromagnetic high-spin state (t2g5-xeg2) for 0<x<0.39, the ferromagnetic high-spin state (t2g5eg2-x) for 0.39⩽x<0.52, followed by the ferromagnetic high-spin-low-spin ordered state (t2g5-xeg2-t2g6eg1-x) for 0.52⩽x<1.1. The two spin-state transitions in the doping range (0<x<1.1) we studied are in agreement with experimental observations.

Nonlinear optical properties of perovskiteYMnO3studied by real-space recursion method

New types of second-order nonlinear optical properties of hexagonal ${\mathrm{YMnO}}_{3}$ have been studied, caused by the coexistence of the noncentrosymmetric ferroelectric ordering of charges and the centrosymmetric spin ordering below its Neel temperature ${T}_{N}.$ Using time-dependent perturbation theory and the Green's function method, we have derived an expression for the nonlinear optical susceptibility in terms of the real-space Green's function. Then, based upon the multiband Hubbard Hamiltonian and the unrestricted Hartree-Fock approximation, the real-space recursion method has been used to calculate the electric structure of ${\mathrm{YMnO}}_{3}$ below ${T}_{N},$ and its nonlinear optical susceptibility. The calculated results are very consistent with the experimental observation, and clearly show different contributions to the nonlinear optical response from the Mn ${e}_{g}$ and O$p$ bands in ${\mathrm{YMnO}}_{3}.$

The effect of Sr doping on the magnetic properties of Co perovskite

Within the unrestricted Hartree–Fock approximation and the real space recursion method, we calculated the electronic structure of the La 1−xSr xCoO 3 in whole doping range 0.0≤ x≤1.0. The low-spin (LS, t 2 g 6 e g 0), the intermediate-spin (IS, t 2 g 5 e g 1), and the high-spin (HS, t 2 g 4 e g 2) states as well as their combinations in the doubled cell were taken as the initial configurations. It is found that the system is a nonmagnetic low-spin state ( t 2 g 6− x e g 0) for x≤0.25 and a ferromagnetic intermediate-spin state ( t 2 g 5 e g 1− x ) for 0.25< x≤0.41. For 0.41< x<0.95, the ground state of the system is a IS–HS ( t 2 g 5 e g 1− x - t 2 g 4 e g 2− x ) nearest neighbor ferromagnetically ordered state, which is followed by the HS state up to x=1.0. The ground state properties as a function of Sr doping are in accord with the experimental observations.